Final answer:
The greatest magnitude of the resultant force when combining two forces occurs when both forces are applied in the same direction. Option (a), where two people push a box in the same direction, would provide a resultant of 10 N + 15 N = 25 N, which is the highest possible resultant.
Step-by-step explanation:
When considering the combination of two forces and determining the greatest magnitude of the resultant force, it's important to understand how vector addition works. The greatest resultant occurs when two forces are applied in the same direction. In this case, the resultant is simply the sum of the individual forces. When two forces are applied in opposite directions, they subtract from each other, leading to a smaller resultant force. If the forces are applied perpendicular to each other, like upwards and to the right, the resultant can be determined by using the Pythagorean theorem, but it will not exceed the sum of the two forces.
- When two people push the box in the same direction, the resultant force is the sum of the individual forces, thus it's 10 N + 15 N = 25 N.
- When one person pushes to the left and the other to the right, the forces oppose each other and partially cancel out, thus the resultant force will be the difference, 15 N - 10 N = 5 N.
- When one person pushes up and the other to the right, the forces are perpendicular and the resultant force is found using the Pythagorean theorem, which would be less than 25 N.
- Lastly, when one person pushes to the left and the other pushes down, the situation is similar to the forces being perpendicular, and the resultant would also be less than 25 N.
Therefore, option (a) When two people push the box to the same direction would produce the greatest magnitude of the resultant force.